Thursday, March 7, 2024

Stock and flow diagrams, a different way to represent dynamical systems

Stock and flow diagrams (see also here) are  a way to represent dynamical system which is the same area covered by EPN ((Extended Petri Nets). They were brought to my attention by the talk John Baez gave at  Edinburgh Mathematical Society last December. Fortunately the talk is available on Youtube.

Although I find that the visuals of EPN are more expressive and the accompanying infrastructure is easier for engineers to comprehend, I have come to realize that listening to the talk is incredibly instructive when it comes to realize that EPN falls in the objects of category theory. An intriguing aspect explored in the talk is the representation of open systems within stock-flow graphs. In EPN, it is assumed that a flow box not originating from a place indicates that the system is open. Additionally, when one EPN features an outgoing flow labeled A and another EPN has an input flow with the same label, they can be combined to create a composite graph. However, in this presentation, a new rectangular symbol is introduced for the same purpose.
Personally, I find the solution in EPN more intuitive, although it may be considered less abstract. Nevertheless, I have come to realize that a similar graphical approach could prove beneficial in extending EPN to represent not only ODE systems but also PDE systems.

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